ISC 2022 Mathematics - Specimen paper (Semester 1), Paper 1 with Answers
All 33 questions of the ISC 2022 Mathematics - Specimen paper (Semester 1), Paper 1, in printed order. Open a question to read it in full and see its answer.
- Q1 The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = \sin(3x + 2)$, $\forall x \in \mathbb{R}$ is: 2 marks · MCQ
- Q2 What will be the Principal value of $\operatorname{cosec}^{-1}(-\sqrt{2})$? 2 marks · MCQ
- Q3 If set A contains 5 elements and set B contains 6 elements, then the number of one-one onto mappings from A to B is: 2 marks · MCQ
- Q4 If $\alpha \le 2\sin^{-1} x + \cos^{-1} x \le \beta$, then $(\alpha, \beta)$ is: 2 marks · MCQ
- Q5 Let A be the set of all students of a boy’s school. Then the relation R in A is defined by… 2 marks · MCQ
- Q6 $\forall x \in \mathbb{R}$, $\cot^{-1}(-x) =$ 2 marks · MCQ
- Q7 The value of $\begin{vmatrix} 1 & \log_a b \\ \log_b a & 1 \end{vmatrix}$ is: 2 marks · MCQ
- Q8 From the matrix equation $AB = AC$, it can be concluded that $B = C$ provided: 2 marks · MCQ
- Q9 What is the transpose of a column matrix? 2 marks · MCQ
- Q10 What is the multiplicative inverse of matrix $A$? 2 marks · MCQ
- Q11 If $A$ and $B$ are two non singular matrices, and $AB$ exists, then $(AB)^{-1}$ is: 2 marks · MCQ
- Q12 If $\Delta = \begin{vmatrix} a & b & c \\ x & y & z \\ p & q & r \end{vmatrix}$, then… 2 marks · MCQ
- Q13 If $y = t^2$ and $t = x + 3$ then $\frac{dy}{dx}$ is equal to: 2 marks · MCQ
- Q14 The set of points, where the function $f(x) = x |x|$ is differentiable in: 2 marks · MCQ
- Q15 If $\sin^{-1} x + \sin^{-1} y = \frac{\pi}{2}$, then $\frac{dy}{dx}$ is equal to: 2 marks · MCQ
- Q16 The value of $\lim_{x \to 0} \frac{\log(1+x)}{x}$ is equal to: 2 marks · MCQ
- Q17 What will be the value of $x$ for the determinant equation… 2 marks · MCQ
- Q18 Any tangent to the curve $y = 3x^7 + 5x + 3$ : 2 marks · MCQ
- Q19 The second derivative of $y = x^3 - 5x^2 + x$ is: 2 marks · MCQ
- Q20 What will be the derivative of $\sin^{-1}\left(\frac{2x}{1+x^2}\right)$ with respect to… 2 marks · MCQ
- Q21 Ramu purchased 5 pens, 3 bags and 1 instrument box and paid ₹ 16. From the same shop Venkat purchased 2 pens , 1 bag and 3… 8 marks · Case based
- Q22 A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window as shown in the figure… 8 marks · Case based
- Q23 Consider the mapping $f: A \to B$ is defined by $f(x) = \frac{x-1}{x-2}$ such that $f(x)$ is one-one onto. Based on the above… 8 marks · Case based
- Q24 What will be the value of m if the vector $2\hat{i} + m\hat{j} + \hat{k}$ is perpendicular to $2\hat{i} - \hat{j} + 3\hat{k}$? 2 marks · MCQ
- Q25 What will be the angle between the two lines $\frac{-x+2}{-2} = \frac{y-1}{7} = \frac{z+3}{-3}$ and… 2 marks · MCQ
- Q26 What are the direction ratios of the line passing through two points (-2, 4, 5) and (1, 2, 3)? 2 marks · MCQ
- Q27 The equation of the line passing (1, -1, 0) and parallel to the line $\frac{x-1}{1} = \frac{y+2}{-2} = \frac{z+1}{-1}$ is: 2 marks · MCQ
- Q28 The given figure shows an air plant holder which is in the shape of a tetrahedron. Let $A(1, 1, 1)$, $B(2, 1, 3)$, $C(3, 2, 2)$ &… 8 marks · Case based
- Q29 A company sells its product for ₹ 20 per unit. Fixed costs for the company is ₹ 45,000 and variable costs is estimated to run 25%… 2 marks · MCQ
- Q30 The demand function for a certain commodity is given by $p = 4000 - 100x$. What will be the total revenue from the sale of 3… 2 marks · MCQ
- Q31 A company sells $x$ packets of biscuits each day at ₹ 10 a packet. The cost of manufacturing these packets is ₹ 5 per packet plus… 2 marks · MCQ
- Q32 The cost function of a firm is given by $C(x) = 3x^2 - 2x + 6$. The average cost of the firm at $x = 3$ is: 2 marks · MCQ
- Q33 The demand function for a certain product is represented by the equation: $p = ax^2 + bx + c$ where $x$ is the number of units… 8 marks · Case based